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# Sort array after converting elements to their squares

• Difficulty Level : Easy
• Last Updated : 28 Jun, 2021

Given an array of both positive and negative integers ‘arr[]’ which are sorted. The task is to sort the square of the numbers of the Array.
Examples:

```Input  : arr[] =  {-6, -3, -1, 2, 4, 5}
Output : 1, 4, 9, 16, 25, 36

Input  : arr[] = {-5, -4, -2, 0, 1}
Output : 0, 1, 4, 16, 25```

Simple solution is to first convert each array element into its square and then apply any “O(nlogn)” sorting algorithm to sort the array elements.

Below is the implementation of the above idea

## C++

 `// C++ program to Sort square of the numbers``// of the array``#include ``using` `namespace` `std;` `// Function to sort an square array``void` `sortSquares(``int` `arr[], ``int` `n)``{``    ``// First convert each array elements``    ``// into its square``    ``for` `(``int` `i = 0; i < n; i++)``        ``arr[i] = arr[i] * arr[i];` `    ``// Sort an array using "sort STL function "``    ``sort(arr, arr + n);``}` `// Driver program to test above function``int` `main()``{``    ``int` `arr[] = { -6, -3, -1, 2, 4, 5 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);` `    ``cout << ``"Before sort "` `<< endl;``    ``for` `(``int` `i = 0; i < n; i++)``        ``cout << arr[i] << ``" "``;``    ``sortSquares(arr, n);` `    ``cout << ``"\nAfter Sort "` `<< endl;``    ``for` `(``int` `i = 0; i < n; i++)``        ``cout << arr[i] << ``" "``;` `    ``return` `0;``}`

## Java

 `// Java program to Sort square of the numbers``// of the array``import` `java.util.*;``import` `java.io.*;` `class` `GFG {``    ``// Function to sort an square array``    ``public` `static` `void` `sortSquares(``int` `arr[])``    ``{``        ``int` `n = arr.length;` `        ``// First convert each array elements``        ``// into its square``        ``for` `(``int` `i = ``0``; i < n; i++)``            ``arr[i] = arr[i] * arr[i];` `        ``// Sort an array using "inbuild sort function"``        ``// in Arrays class.``        ``Arrays.sort(arr);``    ``}` `    ``// Driver program to test above function``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `arr[] = { -``6``, -``3``, -``1``, ``2``, ``4``, ``5` `};``        ``int` `n = arr.length;` `        ``System.out.println(``"Before sort "``);``        ``for` `(``int` `i = ``0``; i < n; i++)``            ``System.out.print(arr[i] + ``" "``);` `        ``sortSquares(arr);``        ``System.out.println(``""``);``        ``System.out.println(``"After Sort "``);``        ``for` `(``int` `i = ``0``; i < n; i++)``            ``System.out.print(arr[i] + ``" "``);``    ``}``}`

## Python3

 `# Python program to Sort square``# of the numbers of the array` `# Function to sort an square array``def` `sortSquare(arr, n):` `    ``# First convert each array``    ``# elements into its square``    ``for` `i ``in` `range``(n):``        ``arr[i]``=` `arr[i] ``*` `arr[i]``    ``arr.sort()` `# Driver code``arr ``=` `[``-``6``, ``-``3``, ``-``1``, ``2``, ``4``, ``5``]``n ``=` `len``(arr)` `print``(``"Before sort"``)``for` `i ``in` `range``(n):``    ``print``(arr[i], end ``=` `" "``)` `print``(``"\n"``)` `sortSquare(arr, n)` `print``(``"After sort"``)``for` `i ``in` `range``(n):``    ``print``(arr[i], end ``=` `" "``)` `# This code is contributed by``# Shrikant13`

## C#

 `// C# program to Sort square``// of the numbers of the array``using` `System;` `class` `GFG {` `    ``// Function to sort``    ``// an square array``    ``public` `static` `void` `sortSquares(``int``[] arr)``    ``{``        ``int` `n = arr.Length;` `        ``// First convert each array``        ``// elements into its square``        ``for` `(``int` `i = 0; i < n; i++)``            ``arr[i] = arr[i] * arr[i];` `        ``// Sort an array using``        ``// "inbuild sort function"``        ``// in Arrays class.``        ``Array.Sort(arr);``    ``}` `    ``// Driver Code``    ``public` `static` `void` `Main()``    ``{``        ``int``[] arr = { -6, -3, -1,``                      ``2, 4, 5 };``        ``int` `n = arr.Length;` `        ``Console.WriteLine(``"Before sort "``);``        ``for` `(``int` `i = 0; i < n; i++)``            ``Console.Write(arr[i] + ``" "``);` `        ``sortSquares(arr);``        ``Console.WriteLine(``""``);``        ``Console.WriteLine(``"After Sort "``);` `        ``for` `(``int` `i = 0; i < n; i++)``            ``Console.Write(arr[i] + ``" "``);``    ``}``}` `// This code is contributed by anuj_67.`

## Javascript

 ``

Output:

```Before sort
-6 -3 -1 2 4 5
After Sort
1 4 9 16 25 36```

Time complexity: O(n log n)

Efficient solution is based on the fact that the given array is already sorted. We do the following two steps.

1. Divide the array into two-part “Negative and positive “.
2. Use merge function to merge two sorted arrays into a single sorted array.

Below is the implementation of the above idea.

## C++

 `// C++ program to Sort square of the numbers of the array``#include ``using` `namespace` `std;` `// function to sort array after doing squares of elements``void` `sortSquares(``int` `arr[], ``int` `n)``{``    ``// first dived array into part negative and positive``    ``int` `K = 0;``    ``for` `(K = 0; K < n; K++)``        ``if` `(arr[K] >= 0)``            ``break``;` `    ``// Now do the same process that we learn``    ``// in merge sort to merge to two sorted array``    ``// here both two half are sorted and we traverse``    ``// first half in reverse meaner because``    ``// first half contain negative element``    ``int` `i = K - 1; ``// Initial index of first half``    ``int` `j = K; ``// Initial index of second half``    ``int` `ind = 0; ``// Initial index of temp array` `    ``// store sorted array``    ``int` `temp[n];``    ``while` `(i >= 0 && j < n) {``        ``if` `(arr[i] * arr[i] < arr[j] * arr[j]) {``            ``temp[ind] = arr[i] * arr[i];``            ``i--;``        ``}``        ``else` `{``            ``temp[ind] = arr[j] * arr[j];``            ``j++;``        ``}``        ``ind++;``    ``}` `    ``/* Copy the remaining elements of first half */``    ``while` `(i >= 0) {``        ``temp[ind] = arr[i] * arr[i];``        ``i--;``        ``ind++;``    ``}` `    ``/* Copy the remaining elements of second half */``    ``while` `(j < n) {``        ``temp[ind] = arr[j] * arr[j];``        ``j++;``        ``ind++;``    ``}` `    ``// copy 'temp' array into original array``    ``for` `(``int` `i = 0; i < n; i++)``        ``arr[i] = temp[i];``}` `// Driver program to test above function``int` `main()``{``    ``int` `arr[] = { -6, -3, -1, 2, 4, 5 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);` `    ``cout << ``"Before sort "` `<< endl;``    ``for` `(``int` `i = 0; i < n; i++)``        ``cout << arr[i] << ``" "``;``    ``sortSquares(arr, n);` `    ``cout << ``"\nAfter Sort "` `<< endl;``    ``for` `(``int` `i = 0; i < n; i++)``        ``cout << arr[i] << ``" "``;` `    ``return` `0;``}`

## Java

 `// Java program to Sort square of the numbers``// of the array``import` `java.util.*;``import` `java.io.*;` `class` `GFG {``    ``// Function to sort an square array``    ``public` `static` `void` `sortSquares(``int` `arr[])``    ``{``        ``int` `n = arr.length;``        ``// first dived array into part negative and positive``        ``int` `k;``        ``for` `(k = ``0``; k < n; k++) {``            ``if` `(arr[k] >= ``0``)``                ``break``;``        ``}` `        ``// Now do the same process that we learn``        ``// in merge sort to merge to two sorted array``        ``// here both two half are sorted and we traverse``        ``// first half in reverse meaner because``        ``// first half contain negative element``        ``int` `i = k - ``1``; ``// Initial index of first half``        ``int` `j = k; ``// Initial index of second half``        ``int` `ind = ``0``; ``// Initial index of temp array` `        ``int``[] temp = ``new` `int``[n];``        ``while` `(i >= ``0` `&& j < n) {``            ``if` `(arr[i] * arr[i] < arr[j] * arr[j]) {``                ``temp[ind] = arr[i] * arr[i];``                ``i--;``            ``}``            ``else` `{` `                ``temp[ind] = arr[j] * arr[j];``                ``j++;``            ``}``            ``ind++;``        ``}` `        ``while` `(i >= ``0``) {``            ``temp[ind++] = arr[i] * arr[i];``            ``i--;``        ``}``        ``while` `(j < n) {``            ``temp[ind++] = arr[j] * arr[j];``            ``j++;``        ``}` `        ``// copy 'temp' array into original array``        ``for` `(``int` `x = ``0``; x < n; x++)``            ``arr[x] = temp[x];``    ``}` `    ``// Driver program to test above function``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `arr[] = { -``6``, -``3``, -``1``, ``2``, ``4``, ``5` `};``        ``int` `n = arr.length;` `        ``System.out.println(``"Before sort "``);``        ``for` `(``int` `i = ``0``; i < n; i++)``            ``System.out.print(arr[i] + ``" "``);` `        ``sortSquares(arr);``        ``System.out.println(``""``);``        ``System.out.println(``"After Sort "``);``        ``for` `(``int` `i = ``0``; i < n; i++)``            ``System.out.print(arr[i] + ``" "``);``    ``}``}`

## Python3

 `# Python3 program to Sort square of the numbers of the array` `# function to sort array after doing squares of elements``def` `sortSquares(arr, n):``    ` `    ``# first dived array into part negative and positive``    ``K ``=` `0``    ``for` `K ``in` `range``(n):``        ``if` `(arr[K] >``=` `0` `):``            ``break``    ` `    ``# Now do the same process that we learn``    ``# in merge sort to merge to two sorted array``    ``# here both two half are sorted and we traverse``    ``# first half in reverse meaner because``    ``# first half contain negative element``    ``i ``=` `K ``-` `1` `# Initial index of first half``    ``j ``=` `K ``# Initial index of second half``    ``ind ``=` `0` `# Initial index of temp array``    ` `    ``# store sorted array``    ``temp ``=` `[``0``]``*``n``    ``while` `(i >``=` `0` `and` `j < n):``        ` `        ``if` `(arr[i] ``*` `arr[i] < arr[j] ``*` `arr[j]):``            ``temp[ind] ``=` `arr[i] ``*` `arr[i]``            ``i ``-``=` `1``        ` `        ``else``:``            ` `            ``temp[ind] ``=` `arr[j] ``*` `arr[j]``            ``j ``+``=` `1``            ` `        ``ind ``+``=` `1``    ` `    ``''' Copy the remaining elements of first half '''``    ``while` `(i >``=` `0``):``        ` `        ``temp[ind] ``=` `arr[i] ``*` `arr[i]``        ``i ``-``=` `1``        ``ind ``+``=` `1``        ` `    ``''' Copy the remaining elements of second half '''``    ``while` `(j < n):``        ``temp[ind] ``=` `arr[j] ``*` `arr[j]``        ``j ``+``=` `1``        ``ind ``+``=` `1``        ` `    ``# copy 'temp' array into original array``    ``for` `i ``in` `range``(n):``        ``arr[i] ``=` `temp[i]` `# Driver code``arr ``=` `[``-``6``, ``-``3``, ``-``1``, ``2``, ``4``, ``5` `]``n ``=` `len``(arr)` `print``(``"Before sort "``)``for` `i ``in` `range``(n):``    ``print``(arr[i], end ``=``" "` `)``    ` `sortSquares(arr, n)``print``(``"\nAfter Sort "``)``for` `i ``in` `range``(n):``    ``print``(arr[i], end ``=``" "` `)` `# This code is contributed by shubhamsingh10`

## C#

 `// C# program to Sort square of the numbers``// of the array``using` `System;` `class` `GFG {` `    ``// Function to sort an square array``    ``public` `static` `void` `sortSquares(``int``[] arr)``    ``{``        ``int` `n = arr.Length;` `        ``// first dived array into part negative and positive``        ``int` `k;``        ``for` `(k = 0; k < n; k++) {``            ``if` `(arr[k] >= 0)``                ``break``;``        ``}` `        ``// Now do the same process that we learn``        ``// in merge sort to merge to two sorted array``        ``// here both two half are sorted and we traverse``        ``// first half in reverse meaner because``        ``// first half contain negative element``        ``int` `i = k - 1; ``// Initial index of first half``        ``int` `j = k; ``// Initial index of second half``        ``int` `ind = 0; ``// Initial index of temp array` `        ``int``[] temp = ``new` `int``[n];``        ``while` `(i >= 0 && j < n) {``            ``if` `(arr[i] * arr[i] < arr[j] * arr[j]) {``                ``temp[ind] = arr[i] * arr[i];``                ``i--;``            ``}``            ``else` `{``                ``temp[ind] = arr[j] * arr[j];``                ``j++;``            ``}``            ``ind++;``        ``}` `        ``while` `(i >= 0) {``            ``temp[ind++] = arr[i] * arr[i];``            ``i--;``        ``}``        ``while` `(j < n) {``            ``temp[ind++] = arr[j] * arr[j];``            ``j++;``        ``}` `        ``// copy 'temp' array into original array``        ``for` `(``int` `x = 0; x < n; x++)``            ``arr[x] = temp[x];``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main(String[] args)``    ``{``        ``int``[] arr = { -6, -3, -1, 2, 4, 5 };``        ``int` `n = arr.Length;` `        ``Console.WriteLine(``"Before sort "``);``        ``for` `(``int` `i = 0; i < n; i++)``            ``Console.Write(arr[i] + ``" "``);` `        ``sortSquares(arr);``        ``Console.WriteLine(``""``);``        ``Console.WriteLine(``"After Sort "``);``        ``for` `(``int` `i = 0; i < n; i++)``            ``Console.Write(arr[i] + ``" "``);``    ``}``}` `// This code is contributed by 29AjayKumar`

## Javascript

 ``

Output

```Before sort
-6 -3 -1 2 4 5
After Sort
1 4 9 16 25 36```

Time complexity: O(n)
space complexity: O(n)

Method 3 –
Another efficient solution is based on the two-pointer method as the array is already sorted we can compare the first and last element to check which is bigger and proceed with the result.

Algorithm –

• Initialize left=0 and right=n-1
• if abs(left) >= abs(right) then store square(arr[left])
at the end of result array and increment left pointer
• else store square(arr[right]) in the result array and decrement right pointer
• decrement index of result array

## C++

 `// CPP code for the above approach``#include ``using` `namespace` `std;` `// Function to sort an square array``void` `sortSquares(vector<``int``>& arr, ``int` `n)``{``    ``int` `left = 0, right = n - 1;``    ``int` `result[n];` `    ``// Iterate from n - 1 to 0``    ``for` `(``int` `index = n - 1; index >= 0; index--) {``      ` `        ``// Check if abs(arr[left]) is greater``        ``// than arr[right]``        ``if` `(``abs``(arr[left]) > arr[right]) {``            ``result[index] = arr[left] * arr[left];``            ``left++;``        ``}``        ``else` `{``            ``result[index] = arr[right] * arr[right];``            ``right--;``        ``}``    ``}``    ``for` `(``int` `i = 0; i < n; i++)``        ``arr[i] = result[i];``}` `// Driver Code``int` `main()``{``    ``vector<``int``> arr;``    ``arr.push_back(-6);``    ``arr.push_back(-3);``    ``arr.push_back(-1);``    ``arr.push_back(2);``    ``arr.push_back(4);``    ``arr.push_back(5);` `    ``int` `n = 6;` `    ``cout << ``"Before sort "` `<< endl;``    ``for` `(``int` `i = 0; i < n; i++)``        ``cout << arr[i] << ``" "``;` `    ``sortSquares(arr, n);``    ``cout << endl;``    ``cout << ``"After Sort "` `<< endl;``    ``for` `(``int` `i = 0; i < n; i++)``        ``cout << arr[i] << ``" "``;``    ``return` `0;``}` `// this code is contributed by Manu Pathria`

## Java

 `// Java program to Sort square of``// the numbers of the array``import` `java.util.*;``import` `java.io.*;` `class` `GFG{``    ` `// Function to sort an square array``public` `static` `void` `sortSquares(``int` `arr[])``{``    ``int` `n = arr.length, left = ``0``,``        ``right = n - ``1``;``    ` `    ``int` `result[] = ``new` `int``[n];``    ` `    ``for``(``int` `index = n - ``1``; index >= ``0``; index--)``    ``{``        ``if` `(Math.abs(arr[left]) > arr[right])``        ``{``            ``result[index] = arr[left] * arr[left];``            ``left++;``        ``}``        ``else``        ``{``            ``result[index] = arr[right] * arr[right];``            ``right--;``        ``}``    ``}``    ``for``(``int` `i = ``0``; i < n; i++)``        ``arr[i] = result[i];``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``int` `arr[] = { -``6``, -``3``, -``1``, ``2``, ``4``, ``5` `};``    ``int` `n = arr.length;` `    ``System.out.println(``"Before sort "``);``    ``for``(``int` `i = ``0``; i < n; i++)``        ``System.out.print(arr[i] + ``" "``);` `    ``sortSquares(arr);``    ``System.out.println(``""``);``    ``System.out.println(``"After Sort "``);``    ``for``(``int` `i = ``0``; i < n; i++)``        ``System.out.print(arr[i] + ``" "``);``}``}` `// This code is contributed by jinalparmar2382`

## Python3

 `# Python3 program to Sort square of the numbers of the array` `# function to sort array after doing squares of elements``def` `sortSquares(arr, n):``    ``left, right ``=` `0``, n ``-` `1``    ``index ``=` `n ``-` `1``    ``result ``=` `[``0` `for` `x ``in` `arr]` `    ``while` `index >``=` `0``:` `        ``if` `abs``(arr[left]) >``=` `abs``(arr[right]):``            ``result[index] ``=` `arr[left] ``*` `arr[left]``            ``left ``+``=` `1``        ``else``:``            ``result[index] ``=` `arr[right] ``*` `arr[right]``            ``right ``-``=` `1``        ``index ``-``=` `1``    ` `    ``for` `i ``in` `range``(n):``        ``arr[i] ``=` `result[i]` `# Driver code``arr ``=` `[``-``6``, ``-``3``, ``-``1``, ``2``, ``4``, ``5` `]``n ``=` `len``(arr)` `print``(``"Before sort "``)``for` `i ``in` `range``(n):``    ``print``(arr[i], end ``=``" "` `)``    ` `sortSquares(arr, n)``print``(``"\nAfter Sort "``)``for` `i ``in` `range``(n):``    ``print``(arr[i], end ``=``" "` `)`

## C#

 `// C# program to Sort square of``// the numbers of the array``using` `System;``class` `GFG{``    ` `// Function to sort an square array``public` `static` `void` `sortSquares(``int` `[] arr)``{``  ``int` `n = arr.Length, left = 0,``  ``right = n - 1;``  ``int` `[]result = ``new` `int``[n];` `  ``for``(``int` `index = n - 1;``          ``index >= 0; index--)``  ``{``    ``if` `(Math.Abs(arr[left]) >``        ``arr[right])``    ``{``      ``result[index] = arr[left] *``                      ``arr[left];``      ``left++;``    ``}``    ``else``    ``{``      ``result[index] = arr[right] *``                      ``arr[right];``      ``right--;``    ``}``  ``}``  ``for``(``int` `i = 0; i < n; i++)``    ``arr[i] = result[i];``}` `// Driver code``public` `static` `void` `Main(``string``[] args)``{``  ``int` `[]arr = {-6, -3, -1, 2, 4, 5};``  ``int` `n = arr.Length;``  ``Console.WriteLine(``"Before sort "``);``  ` `  ``for``(``int` `i = 0; i < n; i++)``    ``Console.Write(arr[i] + ``" "``);` `  ``sortSquares(arr);``  ``Console.WriteLine(``""``);``  ``Console.WriteLine(``"After Sort "``);``  ` `  ``for``(``int` `i = 0; i < n; i++)``    ``Console.Write(arr[i] + ``" "``);``}``}` `// This code is contributed by Chitranayal`

## Javascript

 ``

Output

```Before sort
-6 -3 -1 2 4 5
After Sort
1 4 9 16 25 36```

Time complexity: O(n)
Auxiliary Space: O(n)

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